New result for generalized neural networks with additive time-varying delays using free-matrix-based integral inequality method

This paper investigates the problem of stability for generalized neural networks (GNNs) with additive time-varying delays. Different from previous literatures, a new augmented LyapunovKrasovskii functional (LKF) has been constructed. In this LKF, two augmented terms are constructed to establish the interaction among the state vectors with additive time delay upper bounds. In addition, in consideration of the information for two upper bounds, a single and a double integral terms which contain the two upper bounds of additive time-varying delays are firstly introduced to analyze the GNNs. So, based on those treatments, the information about upper bound of additive time-varying delays is sufficiently used. On the other hand, the free-matrix-based integral inequality which can deal with the time-varying delays directly is employed to bound the derivative of the LKF. Based on above works, less conservative criterion is finally derived. Numerical example is provided to show the effectiveness and less conservatism of the proposed results.

[1]  Qing-Long Han,et al.  New Lyapunov-Krasovskii Functionals for Global Asymptotic Stability of Delayed Neural Networks , 2009, IEEE Trans. Neural Networks.

[2]  Ju H. Park,et al.  Analysis on delay-dependent stability for neural networks with time-varying delays , 2013, Neurocomputing.

[3]  Bin Jiang,et al.  LMI-Based Approach for Global Asymptotic Stability Analysis of Recurrent Neural Networks with Various Delays and Structures , 2011, IEEE Transactions on Neural Networks.

[4]  Min Wu,et al.  Free-Matrix-Based Integral Inequality for Stability Analysis of Systems With Time-Varying Delay , 2015, IEEE Transactions on Automatic Control.

[5]  Min Wu,et al.  Delay-Dependent Stability Criteria for Generalized Neural Networks With Two Delay Components , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[6]  Yajuan Liu,et al.  Robust delay-depent stability criteria for uncertain neural networks with two additive time-varying delay components , 2015, Neurocomputing.

[7]  Fuwen Yang,et al.  $H_{\infty }$ Fault Detection for Networked Mechanical Spring-Mass Systems With Incomplete Information , 2016, IEEE Transactions on Industrial Electronics.

[8]  Yong He,et al.  Global exponential stability of neural networks with time-varying delay based on free-matrix-based integral inequality , 2016, Neural Networks.

[9]  Leon O. Chua,et al.  Cellular neural networks: applications , 1988 .

[10]  Derong Liu,et al.  Qualitative Analysis and Synthesis of Recurrent Neural Networks , 2002 .

[11]  Shen-Ping Xiao,et al.  Stability analysis of generalized neural networks with time-varying delays via a new integral inequality , 2015, Neurocomputing.

[12]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[13]  Magdi S. Mahmoud,et al.  New results for global exponential stability of neural networks with varying delays , 2012, Neurocomputing.

[14]  Jian Sun,et al.  Stability analysis of static recurrent neural networks with interval time-varying delay , 2013, Appl. Math. Comput..

[15]  Zhang Yi,et al.  Selectable and Unselectable Sets of Neurons in Recurrent Neural Networks With Saturated Piecewise Linear Transfer Function , 2011, IEEE Transactions on Neural Networks.

[16]  Jun Wang,et al.  An Improved Algebraic Criterion for Global Exponential Stability of Recurrent Neural Networks With Time-Varying Delays , 2008, IEEE Transactions on Neural Networks.

[17]  Yong He,et al.  Delay-dependent stability criteria for linear systems with multiple time delays , 2006 .

[18]  Yong-ming Li,et al.  New mixed-delay-dependent robust stability conditions for uncertain linear neutral systems , 2014 .

[19]  Dan Zhang,et al.  Mixed H∞ and passivity based state estimation for fuzzy neural networks with Markovian-type estimator gain change , 2014, Neurocomputing.

[20]  Fuwen Yang,et al.  H∞ fault detection filtering for mechanical spring-mass systems over networked systems with incomplete information , 2016 .

[21]  Max Q.-H. Meng,et al.  Delay-range-dependent robust H∞ control for uncertain systems with interval time-varying delays , 2010, Neurocomputing.

[22]  Qing-Long Han,et al.  Global asymptotic stability analysis for delayed neural networks using a matrix-based quadratic convex approach , 2014, Neural Networks.

[23]  S. M. Lee,et al.  New augmented Lyapunov–Krasovskii functional approach to stability analysis of neural networks with time-varying delays , 2014 .

[24]  Andrzej Cichocki,et al.  Neural networks for optimization and signal processing , 1993 .

[25]  Zhiqiang Zuo,et al.  On exponential stability analysis for neural networks with time-varying delays and general activation functions , 2012 .

[26]  Huaguang Zhang,et al.  Global Asymptotic Stability of Recurrent Neural Networks With Multiple Time-Varying Delays , 2008, IEEE Transactions on Neural Networks.

[27]  Min Wu,et al.  An improved global asymptotic stability criterion for delayed cellular neural networks , 2006, IEEE Transactions on Neural Networks.

[28]  Wai Keung Wong,et al.  Distributed Synchronization of Coupled Neural Networks via Randomly Occurring Control , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[29]  Huaguang Zhang,et al.  Novel Weighting-Delay-Based Stability Criteria for Recurrent Neural Networks With Time-Varying Delay , 2010, IEEE Transactions on Neural Networks.

[30]  Jianjun Bai,et al.  New delay-dependent robust stability criteria for uncertain neutral systems with mixed delays , 2014, J. Frankl. Inst..

[31]  Qing-Long Han,et al.  Global Asymptotic Stability for a Class of Generalized Neural Networks With Interval Time-Varying Delays , 2011, IEEE Trans. Neural Networks.

[32]  Guo-Ping Liu,et al.  Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays , 2004, Syst. Control. Lett..

[33]  Jin-Hua She,et al.  Delay-dependent exponential stability of delayed neural networks with time-varying delay , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[34]  Ju H. Park,et al.  Improved approaches to stability criteria for neural networks with time-varying delays , 2013, J. Frankl. Inst..

[35]  Guo-Ping Liu,et al.  New Delay-Dependent Stability Criteria for Neural Networks With Time-Varying Delay , 2007, IEEE Transactions on Neural Networks.

[36]  Ju H. Park,et al.  An improved stability criterion for generalized neural networks with additive time-varying delays , 2016, Neurocomputing.

[37]  Shouming Zhong,et al.  New Delay-Dependent Stability Criteria for Neural Networks With Two Additive Time-varying Delay Components , 2012 .

[38]  Ju H. Park,et al.  New and improved results on stability of static neural networks with interval time-varying delays , 2014, Appl. Math. Comput..

[39]  Yong He,et al.  Complete Delay-Decomposing Approach to Asymptotic Stability for Neural Networks With Time-Varying Delays , 2011, IEEE Transactions on Neural Networks.

[40]  Yong He,et al.  Passivity analysis for neural networks with a time-varying delay , 2011, Neurocomputing.

[41]  Yong He,et al.  Stability Analysis for Delayed Neural Networks Considering Both Conservativeness and Complexity , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[42]  Yingmin Jia,et al.  New approaches on stability criteria for neural networks with two additive time-varying delay components , 2013, Neurocomputing.

[43]  James Lam,et al.  A New Criterion of Delay-Dependent Asymptotic Stability for Hopfield Neural Networks With Time Delay , 2008, IEEE Transactions on Neural Networks.

[44]  Yu Zhao,et al.  Asymptotic stability analysis of neural networks with successive time delay components , 2008, Neurocomputing.

[45]  Yong He,et al.  Improved mixed-delay-dependent asymptotic stability criteria for neutral systems , 2015 .

[46]  Shengyuan Xu,et al.  On global asymptotic stability for a class of delayed neural networks , 2012, Int. J. Circuit Theory Appl..

[47]  Qing-Long Han,et al.  New Delay-Dependent Stability Criteria for Neural Networks With Two Additive Time-Varying Delay Components , 2011, IEEE Transactions on Neural Networks.